Collective processes of an ensemble of spin-1/2 particles

Bradley A. Chase and JM Geremia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque NM 87131 USA

Abstract. When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace which grows quadratically with the number of spins. We also derive explicit formulae for expressing arbitrary identical, local decoherence in terms of these states. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including superposition and spin squeezed states, subject to various symmetric but local decoherence models.

Funded by: NSF (PHY-0652877); DOE/Sandia (707291)

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Please follow these links to download the available items in tar-gzip format. The archive of Mathematica notebooks includes derivations of the recursion relation for symmetric quantum maps on qubits presented in the paper. All LaTeX source, including figure files, the history of drafts and revisions to the paper, and correspondence with journals is included in the source archive. Matlab code and data files used to generate figures in the paper is included in the FigureData archive:

• [Mathematica Notebooks] (tar.gz file containing .nb code for Mathematica 6.0)
• [LaTeX Source and Figure Files] (tar.gz file with RevTeX source and pdf and eps figure files)
• [Simulation Code and Data Files] (tar.gz file with Matlab source)

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• [Project Notes] (tar.gz file containing latex source documents)

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